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In the last few weeks, it was reported that mathematician Edward Nelson of Princeton had claimed to show that Peano Arithmetic, one of many possible axiomatic systems for the numbers, was internally inconsistent. Within a short period, his claim and proof were subject to examination by other pure mathematicians, not least Terence Tao of UCLA, who thought Nelson’s argument had potential flaws. Nelson initially defended himself and then, accepting the criticisms, retracted his claim. More details can be found in a post by John Baez on the n-category blog, which initiated a dialog in which both Tao and Nelson participated, and where Nelson announced his retraction. A subsequent discussion of what happened in this dialog and the lessons for the philosophy of mathematics can be found on the blog of Catarina Dutilh Novaes, a discussion to which Tao again contributed, this time on his methods.
This example of fast proposal-criticism-retraction contrasts sharply with mainstream Economics, where an error in deductive reasoning may be pointed out, with neither retraction nor revision nor apparent learning from its adherents 70 years on. Keynes’ criticisms of conventional austerity economics were first uttered in the 1930s, and yet they still have to be repeated. Relcalcitrant ignorance indeed.
One of the key insights of Keynesian economics is that a government is not like a household: Governments can increase their income by increasing their spending, something most households cannot do. Another key insight is that the effect of one person doing something may be very different if many people also do it. To see better at a baseball stadium, for instance, you can stand up, but this only works if the people in front of you stay seated; if everyone stands, you will see no better than if everyone stayed seated. Likewise, the economy-wide effects of individuals saving may be deleterious even when the effects are beneficial for an individual. Keynes called this the savings trap. Instead of learning from such insights, we get a British Prime Minister telling us all in 2011 to save hard and reduce our personal debt, and treating the national budget as if he were running a a household in Grantham.